Vandenhove’s conjecture: 1-to-2 player and finite-to-infinite lifts for positionality

Ascertain whether, for any objective W, if W is positional over Eve-games (respectively, positional over finite games), then W is positional over all games (including possibly infinite, alternating games).

Background

This conjecture addresses whether positional solvability in the simplest settings (single-player or finite arenas) lifts to positional solvability in the full two-player, possibly infinite, graph setting. The paper proves the lift for ω-regular objectives but the conjecture is stated in general.